248 research outputs found
Gravity and Matter in Causal Set Theory
The goal of this paper is to propose an approach to the formulation of
dynamics for causal sets and coupled matter fields. We start from the continuum
version of the action for a Klein-Gordon field coupled to gravity, and rewrite
it first using quantities that have a direct correspondent in the case of a
causal set, namely volumes, causal relations, and timelike lengths, as
variables to describe the geometry. In this step, the local Lagrangian density
for a set of fields is recast into a quasilocal expression
that depends on pairs of causally related points and
is a function of the values of in the Alexandrov set defined by those
points, and whose limit as and approach a common point is .
We then describe how to discretize , and use it to define a
discrete action.Comment: 13 pages, no figures; In version 2, friendlier results than in
version 1 are obtained following much shorter derivation
A Numerical Study of Coulomb Interaction Effects on 2D Hopping Transport
We have extended our supercomputer-enabled Monte Carlo simulations of hopping
transport in completely disordered 2D conductors to the case of substantial
electron-electron Coulomb interaction. Such interaction may not only suppress
the average value of hopping current, but also affect its fluctuations rather
substantially. In particular, the spectral density of current
fluctuations exhibits, at sufficiently low frequencies, a -like increase
which approximately follows the Hooge scaling, even at vanishing temperature.
At higher , there is a crossover to a broad range of frequencies in which
is nearly constant, hence allowing characterization of the current
noise by the effective Fano factor F\equiv S_I(f)/2e \left. For
sufficiently large conductor samples and low temperatures, the Fano factor is
suppressed below the Schottky value (F=1), scaling with the length of the
conductor as . The exponent is significantly
affected by the Coulomb interaction effects, changing from when such effects are negligible to virtually unity when they are
substantial. The scaling parameter , interpreted as the average
percolation cluster length along the electric field direction, scales as when Coulomb interaction effects are negligible
and when such effects are substantial, in
good agreement with estimates based on the theory of directed percolation.Comment: 19 pages, 7 figures. Fixed minor typos and updated reference
Spacelike distance from discrete causal order
Any discrete approach to quantum gravity must provide some prescription as to
how to deduce continuum properties from the discrete substructure. In the
causal set approach it is straightforward to deduce timelike distances, but
surprisingly difficult to extract spacelike distances, because of the unique
combination of discreteness with local Lorentz invariance in that approach. We
propose a number of methods to overcome this difficulty, one of which
reproduces the spatial distance between two points in a finite region of
Minkowski space. We provide numerical evidence that this definition can be used
to define a `spatial nearest neighbor' relation on a causal set, and conjecture
that this can be exploited to define the length of `continuous curves' in
causal sets which are approximated by curved spacetime. This provides evidence
in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio
Emergent Continuum Spacetime from a Random, Discrete, Partial Order
There are several indications (from different approaches) that Spacetime at
the Plank Scale could be discrete. One approach to Quantum Gravity that takes
this most seriously is the Causal Sets Approach. In this approach spacetime is
fundamentally a discrete, random, partially ordered set (where the partial
order is the causal relation). In this contribution, we examine how timelike
and spacelike distances arise from a causal set (in the case that the causal
set is approximated by Minkowski spacetime), and how one can use this to obtain
geometrical information (such as lengths of curves) for the general case, where
the causal set could be approximated by some curved spacetime.Comment: 8 pages, 2 figures, based on talk by P. Wallden at the NEB XIII
conferenc
Sub-electron Charge Relaxation via 2D Hopping Conductors
We have extended Monte Carlo simulations of hopping transport in completely
disordered 2D conductors to the process of external charge relaxation. In this
situation, a conductor of area shunts an external capacitor
with initial charge . At low temperatures, the charge relaxation process
stops at some "residual" charge value corresponding to the effective threshold
of the Coulomb blockade of hopping. We have calculated the r.m.s value
of the residual charge for a statistical ensemble of capacitor-shunting
conductors with random distribution of localized sites in space and energy and
random , as a function of macroscopic parameters of the system. Rather
unexpectedly, has turned out to depend only on some parameter
combination: for negligible Coulomb interaction
and for substantial interaction. (Here
is the seed density of localized states, while is the
dielectric constant.) For sufficiently large conductors, both functions
follow the power law , but with different
exponents: for negligible and
for significant Coulomb interaction. We have been able to derive this law
analytically for the former (most practical) case, and also explain the scaling
(but not the exact value of the exponent) for the latter case. In conclusion,
we discuss possible applications of the sub-electron charge transfer for
"grounding" random background charge in single-electron devices.Comment: 12 pages, 5 figures. In addition to fixing minor typos and updating
references, the discussion has been changed and expande
Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory
We present a computational tool that can be used to obtain the "spatial"
homology groups of a causal set. Localisation in the causal set is seeded by an
inextendible antichain, which is the analog of a spacelike hypersurface, and a
one parameter family of nerve simplicial complexes is constructed by
"thickening" this antichain. The associated homology groups can then be
calculated using existing homology software, and their behaviour studied as a
function of the thickening parameter. Earlier analytical work showed that for
an inextendible antichain in a causal set which can be approximated by a
globally hyperbolic spacetime region, there is a one parameter sub-family of
these simplicial complexes which are homological to the continuum, provided the
antichain satisfies certain conditions. Using causal sets that are approximated
by a set of 2d spacetimes our numerical analysis suggests that these conditions
are generically satisfied by inextendible antichains. In both 2d and 3d
simulations, as the thickening parameter is increased, the continuum homology
groups tend to appear as the first region in which the homology is constant, or
"stable" above the discreteness scale. Below this scale, the homology groups
fluctuate rapidly as a function of the thickening parameter. This provides a
necessary though not sufficient criterion to test for manifoldlikeness of a
causal set.Comment: Latex, 46 pages, 43 .eps figures, v2 numerous changes to content and
presentatio
Sm/Lsm Genes Provide a Glimpse into the Early Evolution of the Spliceosome
The spliceosome, a sophisticated molecular machine involved in the removal of intervening sequences from the coding sections of eukaryotic genes, appeared and subsequently evolved rapidly during the early stages of eukaryotic evolution. The last eukaryotic common ancestor (LECA) had both complex spliceosomal machinery and some spliceosomal introns, yet little is known about the early stages of evolution of the spliceosomal apparatus. The Sm/Lsm family of proteins has been suggested as one of the earliest components of the emerging spliceosome and hence provides a first in-depth glimpse into the evolving spliceosomal apparatus. An analysis of 335 Sm and Sm-like genes from 80 species across all three kingdoms of life reveals two significant observations. First, the eukaryotic Sm/Lsm family underwent two rapid waves of duplication with subsequent divergence resulting in 14 distinct genes. Each wave resulted in a more sophisticated spliceosome, reflecting a possible jump in the complexity of the evolving eukaryotic cell. Second, an unusually high degree of conservation in intron positions is observed within individual orthologous Sm/Lsm genes and between some of the Sm/Lsm paralogs. This suggests that functional spliceosomal introns existed before the emergence of the complete Sm/Lsm family of proteins; hence, spliceosomal machinery with considerably fewer components than today's spliceosome was already functional
- …